Using the properties of exponents, specifically the product of powers property, we can simplify the expression \( x^{1/6} \cdot x^{1/6} \).
The product of powers property states that when multiplying two powers with the same base, you can add their exponents:
\[ x^a \cdot x^b = x^{a+b} \]
In this case, we have:
\[ x^{1/6} \cdot x^{1/6} = x^{(1/6) + (1/6)} = x^{2/6} = x^{1/3} \]
Thus, the expression \( x^{1/6} \cdot x^{1/6} \) is equivalent to \( x^{1/3} \).